非齐次马氏链的禁止概率

基于齐次马氏链禁止概率理论,研究非齐次马氏链禁止概率.经推导得出其基本分解公式和若干结论,并在引入假设条件下,得出非齐次马氏链禁止概率与齐次马氏链禁止概率的联系.     

非齐次马氏链状态无限次返回的充分条件

本文给出非齐次马氏链状态无限次返回的充分条件,在此条件下,以概率1给出了非齐次马氏链转移概率的强大数定律．     

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本文给出非齐次马氏链状态无限次返回的充分条件, 在此条件下, 以概率1给出了非齐次 马氏链转移概率的强大数定律     

三叉树上分支马氏链的等价性质

在二叉树上分支马氏链的等价性质研究的基础上,给出了三叉树上分支马氏链定义的离散形式,除了把二叉树上分支马氏链的两个等价性质平移到三叉树上分支马氏链以外,又给出了三叉树上分支马氏链的两个等价性质及两个性质.得出结论的关键方法是在概率乘积公式及条件概率公式的计算中正确处理其中所涉及到的许多繁杂的必然事件.     

非齐次树上非齐次马氏链的若干强大数定律

通过构造适当的非负鞅,将Doob鞅收敛定理应用于几乎处处收敛的研究,给出了一类非齐次树上m重连续状态非齐次马氏链的若干强大数定律,推广了相关结果.     

一个强极限定理

设是可列非齐次马氏链，本文通过利用［１］中提出的在Ｗｉｅｎｅｒ概率空间的一种实现，而给出了一个对任意可列非齐次马氏链普遍成立的强极限定理。     

可列非齐次马氏链的若干极限定理

非齐次马氏链的极限定理曾被不少作者研究过,在他们的工作中分别对马氏链作了相应的限制(参见[1]—[9])。本文的主要工作是给出对任意非齐次马氏链均成立的一类关于状态和状态序偶出现频率的极限定理。在证明中本文提出了一种与传统方法不同的方法——分割单位区间法,其要点是在Wiener概率空间给出马氏链的一种实现,并定义适当的单调函数,然后应用单调函数导数存在定理来证明有关极限几乎处处存在。     

基于关联面积的变权组合预测方法及其应用

变权组合预测方法是一种应用非常广泛的组合预测方法,它能够有效提高组合预测方法的预测和拟合精度.为了提高拟合精度,利用各个单项预测方法与原始数据序列在两个相邻时刻的关联面积以及关联度,给出了一种确定变权组合预测模型变权重系数的方法.最后利用该变权重的组合预测模型建立了新疆建设兵团城镇化发展水平的变权组合预测模型,结果表明这类变权组合预测方法具有较高的预测和拟合精度.     

考虑征税和利息的绝对破产的马氏调控风险模型

本文考虑马氏调控风险模型.在该模型中,当嵌入的马氏链的状态发生变化时,索赔达到的强度,索赔额的分布和征税的税率也随之发生改变.当盈余为正的时候,保险公司获得无风险投资收益,假定收益率是一正的常数;当盈余为负的时候,保险公司通过借贷来维持其业务,假定借贷利率也是一个正的常数.当保险公司的借贷利息大于保费收入的时候,保险公司就无法继续自己的业务,此时称保险公司绝对破产了.本文给出保险公司的生存概率,总赋税的现值,盈余从负变为零的概率(复苏概率)等特征量满足的解析式,并在一状态的马氏调控风险模型下得到了复苏概率的具体表达式.此外,在指数索赔下,将上述特征量通过数值的方法进行敏感性分析.     

一般状态空间马氏链随机泛函的指数矩

本文研究了一般状态空间马氏链随机泛函的指数矩.利用最小非负解理论,得到了随机泛函的指数矩是相应方程的最小非负解,推广了可数状态空间马氏链的结果,作为应用,证明了随机泛函的指数矩与漂移条件等价.     

Spanning Forests of Digraphs and Limiting Probabilities of Markov Chains

A maximum out forest of a digraph is its spanning subgraph that consists of disjoint diverging trees and has the maximum possible number of arcs. For an arbitrary weighted digraph, we consider a matrix of specific weights of maximum out forests and demonstrate how this matrix can be used to get a graph-theoretic interpretation for the limiting probabilities of Markov chains. For a special (nonclassical) correspondence between Markov chains and weighted digraphs, the matrix of Cesáro limiting transition probabilities of any finite homogeneous Markov chain coincides with the normalized matrix of maximum out forests of the corresponding digraphs. This provides a finite (combinatorial) method to calculate the limiting probabilities of Markov chains and thus their stationary distributions. On the other hand, the Markov chain technique provides the proofs to some statements about digraphs.     

Effects of operator learning on production output: a Markov chain approach

We develop a Markov chain approach to forecast the production output of a human-machine system, while encompassing the effects of operator learning. This approach captures two possible effects of learning: increased production rate and reduced downtime due to human error. In the proposed Markov chain, three scenarios are possible for the machine at each time interval: survival, failure, and repair. To calculate the state transition probabilities, we use a proportional hazards model to calculate the hazard rate, in terms of operator-related factors and machine working age. Given the operator learning curves and their effect on reducing human error over time, the proposed approach is considered to be a non-homogeneous Markov chain. Its result is the expected machine uptime. This quantity, along with production forecasting at various operator skill levels, provides us with the expected production output.     

加权马尔科夫链在鄂尔多斯市年降水量预测中的应用

鄂尔多斯市是内蒙古自治区重要的农牧渔业生产区.本文采用样本均值—标准差分级法,将鄂尔多斯市11个气象站1961-2019年的年降水量序列划分为丰水年、偏丰水年、平水年、偏枯水年,枯水年5个状态;以年降水量序列各阶自相关系数rk为权值,建立了加权马尔科夫预测模型,对鄂尔多斯市2017年、2018年、2019年的年降水量数值和所处状态进行预测.结果显示相对误差分别为1.3%,6.9%,4.5%,预测精度较高,方法得当.于是利用精度检验后的加权马尔科夫模型预测了鄂尔多斯市2020年降水量为312.81mm,划分为平水年.同时利用马尔科夫模型的遍历性,讨论了鄂尔多斯市年降水量的极限分布和丰枯状态重现期.研究结果表明,鄂尔多斯市59a来降水过程中枯水年、偏枯水年、平水年、偏丰水年、丰水年5种状态出现的概率分别为0.1358、0.1941、0.3693、0.1926、0.1083,即出现平水年的可能性最大,重现期为2.71a;出现丰水年的可能性最小,重现期为9.23a.上述研究结果与降水量序列及所处状态是保持一致的,由此可见利用加权马尔科夫链预测鄂尔多斯地区的年降水量是可行且有效的.     

马尔可夫模型的市场预测方法及其应用

本文简述了马尔可夫模型的基本原理，介绍了利用马氏过程的基本特征．即其平稳性和无后效性．对随机现象进行统计预测的方法。本文选取市场为研究对象，根据产品的市场占有率的随机变化过程，建立起市场占有率的马尔可夫预测模型，并进行了实例分析。在模型的实际应用时，要注意系统状态转移的平稳性和进行系统状态划分的有效性。     

Stability and monotonicity for interactive Markov chains

In a Markov chain model of a social process, interest often centers on the distribution of the population by state. One question, the stability question, is whether this distribution converges to an equilibrium value. For an ordinary Markov chain (a chain with constant transition probabilities), complete answers are available. For an interactive Markov chain (a chain which allows the transition probabilities governing each individual to depend on the locations by state of the rest of the population), few stability results are available. This paper presents new results. Roughly, the main result is that an interactive Markov chain with unique equilibrium will be stable if the chain satisfies a certain monotonicity property. The property is a generalization to interactive Markov chains of the standard definition of monotonicity for ordinary Markov chains.     

Success runs of lengthk in Markov dependent trials

The geometric type and inverse Polýa-Eggenberger type distributions of waiting time for success runs of lengthk in two-state Markov dependent trials are derived by using the probability generating function method and the combinatorial method. The second is related to the minimal sufficient partition of the sample space. The first two moments of the geometric type distribution are obtained. Generalizations to ballot type probabilities of which negative binomial probabilities are special cases are considered. Since the probabilities do not form a proper distribution, a modification is introduced and new distributions of orderk for Markov dependent trials are developed.     

客户回报随机过程的Markov性和时间齐次性

在客户发展关系的Markov链模型的基础上,构建了企业的客户回报随机过程．证明了：在适当假设下,客户回报过程是Markov链。甚至是时间齐次的Markov链．本文求出了该链的转移概率．通过转移概率得到了客户给企业期望回报的一些计算公式,从而为企业选定发展客户关系策略提供了有效的量化基础．     

On Finite Markov Chain Imbedding and Its Applications

The finite Markov Chain Imbedding technique has been successfully applied in various fields for finding the exact or approximate distributions of runs and patterns under independent and identically distributed or Markov dependent trials. In this paper, we derive a new recursive equation for distribution of scan statistic using the finite Markov chain imbedding technique. We also address the problem of obtaining transition probabilities of the imbedded Markov chain by introducing a notion termed Double Finite Markov Chain Imbedding where transition probabilities are obtained by using the finite Markov chain imbedding technique again. Applications for random permutation model in chemistry and coupon collector’s problem are given to illustrate our idea.     

The lumpability property for a family of Markov chains on poset block structures

We construct different classes of lumpings for a family of Markov chain products which reflect the structure of a given finite poset. We essentially use combinatorial methods. We prove that, for such a product, every lumping can be obtained from the action of a suitable subgroup of the generalized wreath product of symmetric groups, acting on the underlying poset block structure, if and only if the poset defining the Markov process is totally ordered, and one takes the uniform Markov operator in each factor state space. Finally we show that, when the state space is a homogeneous space associated with a Gelfand pair, the spectral analysis of the corresponding lumped Markov chain is completely determined by the decomposition of the group action into irreducible submodules.